Identifier
Values
[1] => [[1]] => [[1]] => [[1]] => 1
[2] => [[1,2]] => [[1,2]] => [[1,2]] => 2
[1,1] => [[1],[2]] => [[1,2]] => [[1,2]] => 2
[3] => [[1,2,3]] => [[1,2,3]] => [[1,2,3]] => 3
[2,1] => [[1,2],[3]] => [[1,2,3]] => [[1,2,3]] => 3
[1,1,1] => [[1],[2],[3]] => [[1,2],[3]] => [[1,3],[2]] => 3
[4] => [[1,2,3,4]] => [[1,2,3,4]] => [[1,2,3,4]] => 4
[3,1] => [[1,2,3],[4]] => [[1,2,3,4]] => [[1,2,3,4]] => 4
[2,2] => [[1,2],[3,4]] => [[1,2,3,4]] => [[1,2,3,4]] => 4
[2,1,1] => [[1,2],[3],[4]] => [[1,2,3],[4]] => [[1,2,4],[3]] => 4
[1,1,1,1] => [[1],[2],[3],[4]] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 4
[5] => [[1,2,3,4,5]] => [[1,2,3,4,5]] => [[1,2,3,4,5]] => 5
[4,1] => [[1,2,3,4],[5]] => [[1,2,3,4,5]] => [[1,2,3,4,5]] => 5
[3,2] => [[1,2,3],[4,5]] => [[1,2,3,4,5]] => [[1,2,3,4,5]] => 5
[3,1,1] => [[1,2,3],[4],[5]] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 5
[2,2,1] => [[1,2],[3,4],[5]] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 5
[2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 5
[1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 5
[6] => [[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 6
[5,1] => [[1,2,3,4,5],[6]] => [[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 6
[4,2] => [[1,2,3,4],[5,6]] => [[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 6
[4,1,1] => [[1,2,3,4],[5],[6]] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 6
[3,3] => [[1,2,3],[4,5,6]] => [[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 6
[3,2,1] => [[1,2,3],[4,5],[6]] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 6
[3,1,1,1] => [[1,2,3],[4],[5],[6]] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 6
[2,2,2] => [[1,2],[3,4],[5,6]] => [[1,2,3,4],[5,6]] => [[1,2,3,6],[4,5]] => 6
[2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 6
[2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 6
[1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 6
[7] => [[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => 7
[6,1] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => 7
[5,2] => [[1,2,3,4,5],[6,7]] => [[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => 7
[5,1,1] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 7
[4,3] => [[1,2,3,4],[5,6,7]] => [[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => 7
[4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 7
[4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 7
[3,3,1] => [[1,2,3],[4,5,6],[7]] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 7
[3,2,2] => [[1,2,3],[4,5],[6,7]] => [[1,2,3,4,5],[6,7]] => [[1,2,3,4,7],[5,6]] => 7
[3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 7
[3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 7
[2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,2,3,4],[5,6],[7]] => [[1,2,3,7],[4,5],[6]] => 7
[2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 7
[2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 7
[1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 7
[8] => [[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 8
[7,1] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 8
[6,2] => [[1,2,3,4,5,6],[7,8]] => [[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 8
[6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 8
[5,3] => [[1,2,3,4,5],[6,7,8]] => [[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 8
[5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 8
[5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 8
[4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 8
[4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 8
[4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[1,2,3,4,5,6],[7,8]] => [[1,2,3,4,5,8],[6,7]] => 8
[4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 8
[4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 8
[3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[1,2,3,4,5,6],[7,8]] => [[1,2,3,4,5,8],[6,7]] => 8
[3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 8
[3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,2,3,4,5],[6,7],[8]] => [[1,2,3,4,8],[5,6],[7]] => 8
[3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 8
[3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 8
[2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,2,3,4],[5,6],[7,8]] => [[1,2,3,8],[4,5],[6,7]] => 8
[2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,2,3,4],[5,6],[7],[8]] => [[1,2,3,8],[4,5],[6],[7]] => 8
[2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 8
[2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 8
[1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 8
[9] => [[1,2,3,4,5,6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[7,2] => [[1,2,3,4,5,6,7],[8,9]] => [[1,2,3,4,5,6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,9],[8]] => 9
[6,3] => [[1,2,3,4,5,6],[7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,9],[8]] => 9
[6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,9],[7],[8]] => 9
[5,4] => [[1,2,3,4,5],[6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,9],[8]] => 9
[5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [[1,2,3,4,5,6,7],[8,9]] => [[1,2,3,4,5,6,9],[7,8]] => 9
[5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,9],[7],[8]] => 9
[5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,2,3,4,5,9],[6],[7],[8]] => 9
[4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,9],[8]] => 9
[4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [[1,2,3,4,5,6,7],[8,9]] => [[1,2,3,4,5,6,9],[7,8]] => 9
[4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,9],[7],[8]] => 9
[4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,2,3,4,5,9],[6,7],[8]] => 9
[4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,2,3,4,5,9],[6],[7],[8]] => 9
[4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,2,3,4,9],[5],[6],[7],[8]] => 9
[3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [[1,2,3,4,5,6],[7,8,9]] => [[1,2,3,4,5,9],[6,7,8]] => 9
[3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,2,3,4,5,9],[6,7],[8]] => 9
[3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,2,3,4,5,9],[6],[7],[8]] => 9
[3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [[1,2,3,4,5],[6,7],[8,9]] => [[1,2,3,4,9],[5,6],[7,8]] => 9
[3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,2,3,4,9],[5,6],[7],[8]] => 9
[3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,2,3,4,9],[5],[6],[7],[8]] => 9
[3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,2,3,9],[4],[5],[6],[7],[8]] => 9
[2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,2,3,9],[4,5],[6,7],[8]] => 9
[2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,2,3,9],[4,5],[6],[7],[8]] => 9
[2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,2,3,9],[4],[5],[6],[7],[8]] => 9
[2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 9
[1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 9
[10] => [[1,2,3,4,5,6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,10],[9]] => 10
[7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
>>> Load all 140 entries. <<<
[7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,10],[9]] => 10
[7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,10],[8],[9]] => 10
[6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,10],[9]] => 10
[6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [[1,2,3,4,5,6,7,8],[9,10]] => [[1,2,3,4,5,6,7,10],[8,9]] => 10
[6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,10],[8],[9]] => 10
[6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,2,3,4,5,6,10],[7],[8],[9]] => 10
[5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,10],[9]] => 10
[5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [[1,2,3,4,5,6,7,8],[9,10]] => [[1,2,3,4,5,6,7,10],[8,9]] => 10
[5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,10],[8],[9]] => 10
[5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,2,3,4,5,6,10],[7,8],[9]] => 10
[5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,2,3,4,5,6,10],[7],[8],[9]] => 10
[5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,2,3,4,5,10],[6],[7],[8],[9]] => 10
[4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [[1,2,3,4,5,6,7,8],[9,10]] => [[1,2,3,4,5,6,7,10],[8,9]] => 10
[4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,10],[8],[9]] => 10
[4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [[1,2,3,4,5,6,7],[8,9,10]] => [[1,2,3,4,5,6,10],[7,8,9]] => 10
[4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,2,3,4,5,6,10],[7,8],[9]] => 10
[4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,2,3,4,5,6,10],[7],[8],[9]] => 10
[4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [[1,2,3,4,5,6],[7,8],[9,10]] => [[1,2,3,4,5,10],[6,7],[8,9]] => 10
[4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,2,3,4,5,10],[6,7],[8],[9]] => 10
[4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,2,3,4,5,10],[6],[7],[8],[9]] => 10
[4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,2,3,4,10],[5],[6],[7],[8],[9]] => 10
[3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [[1,2,3,4,5,6],[7,8,9],[10]] => [[1,2,3,4,5,10],[6,7,8],[9]] => 10
[3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [[1,2,3,4,5,6],[7,8],[9,10]] => [[1,2,3,4,5,10],[6,7],[8,9]] => 10
[3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,2,3,4,5,10],[6,7],[8],[9]] => 10
[3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,2,3,4,5,10],[6],[7],[8],[9]] => 10
[3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,2,3,4,10],[5,6],[7,8],[9]] => 10
[3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,2,3,4,10],[5,6],[7],[8],[9]] => 10
[3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,2,3,4,10],[5],[6],[7],[8],[9]] => 10
[3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,10],[4],[5],[6],[7],[8],[9]] => 10
[2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [[1,2,3,10],[4,5],[6,7],[8,9]] => 10
[2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,2,3,10],[4,5],[6,7],[8],[9]] => 10
[2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,2,3,10],[4,5],[6],[7],[8],[9]] => 10
[2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,10],[4],[5],[6],[7],[8],[9]] => 10
[2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 10
[1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 10
[12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 12
[6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 12
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The last entry in the first row of a standard tableau.
Map
catabolism
Description
Remove the first row of the standard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
Map
inverse promotion
Description
The inverse promotion of a standard Young tableau.
This map replaces the entry $1$ of the tableau with $n+1$, uses the jeu de taquin to move it to the outer rim, and finally decreases all entries by one.